臺灣博碩士論文加值系統

偽剛體3R模型法(Pseudo-rigid-body 3R model, PRB 3R)為近年被發展出的一種樑分析理論，該方法將樑假想為一個具四桿三接頭的剛性串聯機構，且每個接頭上皆有一扭簧，當樑（即機構）末端受一外力，即可藉由扭簧與桿件之間的力量與位移關係，等效出樑末端受力下的位置與方位。本文應用PRB 3R模型法於一般型平面雙超彈性纜線驅動連續體機構(Continuum mechanism)之位移分析，於給定兩條超彈性纜線長度之條件下，求解末端效應器的位置與方位。本研究並使用ANSYS有限元素分析軟體與實驗驗證其理論分析誤差與效率。分析範圍為纜線初始長度在200至300 mm間、推拉長度在0至50 mm之間、下平板之纜線垂直間距為35至60 mm之間、且上平板之纜線垂直間距為35至40 mm之間。研究結果顯示， PRB 3R模型法與實驗數據相較於ANSYS分析結果之最大位置誤差分別為1.96 %與4.88 %，最大方位誤差分別為2.23 %與4.01 %。在計算效率方面，PRB 3R模型法計算平均時間為0.12秒，而ANSYS分析平均時間為74.6秒，PRB 3R模型法的計算效率明顯優於ANSYS分析時間。

The pseudo-rigid-body 3R model (PRB 3R) is a relatively new method for beam analysis. It considers a beam as a four-bar articulating chain with three revolute joints. Each joint is associated with a torsional spring, which collaboratively bear the applied force at the end point of the chain (i.e., the tip of the beam). Based on suitable ratios of link lengths and spring stiffnesses of the four-bar chain, the displacement of the tip of the beam can be approximated by solving the kinematics and force equations of the four-bar chain. This thesis employs the PRB 3R model to analyze the displacement of the general planar continuum mechanism driven by two superelastic wires. In this study, the lengths of the two superelactic wires are given, and the position and orientation of the end-effector are to be found. A couple of numerical examples with different geometric parameters are studied. The results obtained by using PRB 3R model are verified by ANSYS software and experiments. The boundary conditions for the experiments are that the initial wire lengths are between 200 to 300 mm, the manipulating wire lengths, i.e., the inputs, are from 0 to 50 mm, and the distances between the wire connecting points on the ground and end-effector is from 35 to 60 mm and 35 to 40 mm, respectively. It shows that, as compared to the ANSYS analytical results, the percentage position errors of the PRB 3R model and the experiments are within 1.96% and 4.88%, respectively. And, the percentage orientation errors are within 2.23% and 4.01%, respectively. Furthermore, the program run times of the ANSYS is 74.6 seconds in average, while that of PRB 3R model is 0.12 seconds in average, which obviously much faster than the commercial software ANSYS.

摘要
ABSTRACT
致謝
目錄
表目錄
圖目錄
第一章　緒論
1.1 研究動機
1.2 文獻回顧
1.3 研究目的
1.4 論文架構
第二章　一般型平面雙纜線驅動連續體機構之位移分析
2.1 平面雙纜線驅動連續體機構構造
2.2 問題敘述與基本假設
2.3 偽剛體模型法求解
2.3.1 PRB 3R model基本理論
2.3.2 平面雙纜線驅動連續體機構之PRB 3R model求解
2.4 數值範例
2.5 討論
2.6 小結
第三章　有限元素法驗證
3.1 建模與設定
3.2 收歛性分析
3.3 數值範例驗證
3.4 討論
3.5 小結
第四章　實驗與結果比較
4.1 實驗設備與流程
4.2 實驗模型之參數調整
4.3 實驗結果
4.4 數據比較與驗證
4.5 誤差討論
4.6 小結
第五章　結論與未來展望
5.1 結論
5.2 未來展望
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